House Speaker John Boehner (R) of Ohio speaks at a news conference after a Republican caucus meeting on Capitol Hill in Washington on December 18. Boehner emerged from a meeting with fellow Republicans on Tuesday morning pledging to press forward on talks to avert the 'fiscal cliff,' as hope of a deal rose.

Washington — Even with House Speaker John Boehner of Ohio and President Obama appearing closer than ever to an accord on tax increases, entitlement changes, and spending cuts to avoid the “fiscal cliff,” there is no letup in the game of political hardball being played outside the negotiations.

Tuesday morning, hours after receiving a compromise proposal from Mr. Obama that essentially split the difference between the two sides’ starting positions, Speaker Boehner announced a fallback “Plan B” in which the House, perhaps as early as Thursday, would vote to raise taxes on those earning more than $1 million a year.

The proposal appeared designed at the minimum to put Democrats – many of whom had supported just such a plan in the past – into a political bind, provide cover for the Republicans in the event the negotiations fail, and, in so doing, seek to exert more pressure on the president. The potential floor vote on a tax increase, moreover, could indicate how much support the Speaker could expect for a tax increase as part of a broader compromise with the president.

While Boehner said he would continue to negotiate a deal for avoiding the fiscal cliff of $600 billion in higher taxes and spending cuts slated to begin Jan. 1, his Plan B was quickly rejected by the White House and Democratic leaders in both the House and Senate.

Boehner announced his fallback plan the morning after a White House proposal emerged that backed off the president’s election promise of raising tax rates on household income over $250,000, raising the threshold for higher tax rates to $400,000 per household.

Together with a compromise position on the estate tax and higher rates on capital gains and dividends, among other tax measures, the president’s offer would raise $1.2 trillion in higher taxes over the next decade, at the midpoint of the president’s initial offer of $1.6 trillion and Boehner’s opening offer of $800 billion.

The White House plan offers $930 billion in spending reductions for entitlement programs and broader government spending, with an additional $290 billion in lower interest costs that Republicans are loathe to count as lower spending, that together total $1.2 trillion. At $930 billion, the figure is roughly between the administration’s $300 billion opening offer for entitlement reductions and the speaker’s opening bid of $1.4 trillion.

"Any movement away from the unrealistic offers the president has made previously is a step in the right direction,” said Michael Steel, a Boehner spokesman, “but a proposal that includes $1.3 trillion in revenue for only $930 billion in spending cuts cannot be considered balanced.”

The White House pointed out that the president’s latest offer “reflects real compromise” in its narrowing of the differences between the Democratic and Republican positions.

“That is the essence of compromise,” the White House spokesman, Jay Carney, said in a statement. “The parameters of a deal are clear, and the president is willing to continue to work with Republicans to reach a bipartisan solution that averts the fiscal cliff.”

Boehner, too, said his backup plan would not preclude further fiscal cliff negotiations.

“This is a difficult time for Americans,” Boehner said Tuesday, when asked if the shootings in Newtown, Conn. were impacting the fiscal cliff talks. “That's why we continue to have conversations with the White House. I've continued to have hope that we can reach an agreement.”

With tax increases on the table, however, it isn’t clear that Boehner would be able to clear his Plan B, let alone a compromise deal, through his own conference – the two leaders reportedly reached an accord in the summer of 2011 that was scuttled when Republicans balked at any tax hikes.

This time around, however, Republicans are not openly warring on tax increases.

“Taxes are going up by law anyway so we have to try to make sure they don’t go up on as many people as possible,” said Rep. Paul Broun (R) of Georgia after a meeting with party leadership Tuesday morning.

Rep. Steve Womack (R) of Arkansas, a staunchly conservative freshman, said many in the conference understand the predicament the speaker is in.

He’s dealing with two-thirds of power that’s in [Democratic hands] so he’s got a difficult hand to play,” Representative Womack said, referring to the Democratic White House and Senate. “He’s got difficult negotiations, and on the other hand he’s got a contentious conference to deal with, and I totally understand the position he’s in.”

What Womack said would bring Republicans around to whatever deal is eventually struck is the precision and size of spending reductions.

“If I heard one common theme, it was the lack of clarity on spending,” Womack said in characterizing what rank-and-file Republicans told leadership on Tuesday. “What are we getting in return if indeed we can’t save 100 percent of the electorate from a tax increase?”

But if talks break down, there’s Plan B, which could flip the tax-the-wealthy script on Democrats. In that scenario, House Republicans could pass a tax hike on only those Americans with over $1 million in income, Boehner said.

House Republicans would pick up legislation passed in the Senate earlier this year that raised income tax rates for household income above $250,000, amend it to the $1 million threshold, and then pass it. Fixes to the Alternative Minimum Tax (AMT) and the estate tax, both which need action by year’s end, could be included in that bill, Boehner said.

However, the vote on Thursday would not deal with the "sequester," or $109 billion in spending reductions divided between the Defense Department and discretionary spending, according to Boehner.

That would, if the speaker could muster the Republican votes to pass it, put the GOP in the position so often claimed by Democrats (and, indeed, claimed by Mrs. Pelosi in a letter to the speaker several months ago) of favoring tax rate increases on millionaires instead of across-the-board rate increases that would occur if Congress fails to act.

House Democratic leaders, including minority leader Nancy Pelosi and whip Steny Hoyer, oppose the measure, Congressman Hoyer said Tuesday, and the leaders would push their members to vote against such a move.

Senate majority leader Harry Reid (D) of Nevada said the speaker’s fallback plan would not, in fact, protect anyone because it could not pass the Senate.

“Speaker Boehner’s ‘Plan B’ is the farthest thing from a balanced approach,” Senator Reid said in an e-mailed statement. “It will not protect middle-class families because it cannot pass both Houses of Congress.”

But with 53 Senate Democrats having already voted for just such a tax increase, Republicans appear eager to claim that after 20 years of opposing tax increases of any sort, they were willing to compromise to avoid the fiscal cliff – and Democrats were not.

“For years, Washington Democrats – led by Sen. Schumer and Rep. Nancy Pelosi – have been calling for a bill to stop the tax hikes except on millionaires,” Mr. Steel said. “They even voted in favor of it. To oppose it now would make them entirely responsible for the tax hikes that tens of millions of Americans face in less than two weeks. They know that, and the President knows that.”

Democrats weren’t exactly in the dark about Boehner’s political positioning.

“I think it’s a political ploy to give [Boehner’s] members some way to respond to the public that thinks all the Republicans are doing is protecting the wealthy,” Hoyer said.

Democrats who previously supported the measure, like Sen. Chuck Schumer (D) of New York, said Republicans would have been wise to take them up on the measure when it was originally offered.

"Republicans should've taken Senator Schumer's offer two years ago when they had the chance," said Brian Fallon, a spokesman for the New York Democrat. "We've had an election on the president's tax plan, the president won, and Republicans can't turn the clock back. It's not surprising Republicans are having buyer's remorse, but we need higher revenues now."

But with both the speaker and the president still committed to negotiations, a key question hanging over the House as Christmas approaches is whether the Republicans can muster the votes necessary to pass a tax hike without Democratic support.